The OP has a 43% chance of proving himself correct. He lists 13 out of the 30 teams which is 43%. However, that is still not proof that the lottery is fixed. OTOH, if one of the 17 teams not listed gets the #1, then that does prove he is incorrect.
I'll take it a step further, the OP can create this list every year before the lottery for the next 10 years. If one of the teams on his list is chosen every single year for 10 years, then that still does not prove he is correct. There is a difference between correlation and causation.